Civil Engineering Reference
In-Depth Information
where
t
i
is the wall thickness and and are the first (statical) moments of area
with respect to the neutral axis. The area to be considered is the one which is cut off
from the cross-section by a line parallel to the neutral axis, where the shear stress is
needed, i.e. above (or below) the point considered.
Shear stresses develop from the Saint-Venant torsion as well. The formula for the
k
th wall element of an open cross-section is
(5.70)
where
(5.71)
is the Saint-Venant torsional constant of the cross-section and
t
i,k
and
h
i,k
are the wall
thickness and length of the middle lane of the
k
th wall element of the cross-section of
the
i
th bracing element.
When the ith element has a closed cross-section, the formula for the shear
stresses is
(5.72)
where
s
is the arc length,
A
o
is the area enclosed by the middle line of the wall and
t(s)
is the wall thickness at
s
(Fig. 5.19).
Fig. 5.19
Closed cross-section.
Finally, warping torsion also develops shear stresses:
